We claim that momentum is conserved, yet s.;z+xtmbk 1y zlq3z(7s; fub most moving objects eventually slow down and sto3tbkl(z u yx.qmf7 sz+b;sz1;p. Explain.

When a person jumps from a tree to the ground, what happens to the momentj;h 3*o0e -dhfjnja8 cum of the person up;n0* cojjehdahj-3f 8on striking the ground?

When you release an inflated but untied balloon, why does it fly acrtmc k5 ko(2s4voss the room5 t2(vokck4ms?

It is said that in ancient times a rich man with av rb5u(j v:r,w ve+sf* bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to s fe(u,s* v+:wrjv5vrb hore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space 0gvtk 8i.k/q jand is essentially in a vacuv.j0i8q g kt/kum?

According to Eq. 7–5, the lq(7glq+2 ,w9 suxzpjdonger the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobilqp(qu9jd7 sgxwz, 2+le collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today q((cln9:foebgkkfpz-; z z/ ,, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of th zc(ogp :zqzl-bff 9;k /(nek,is new design?

Why can a batter hit a pitched baseball further thant dit p( ;.y1kg8eio,w a ball tossed in the air by the ba.k;,8 w1deigoy pi(t ttter?

Is it possible for an objecttmeeprps - ;kkgsguef 8,mg s/;(6hn6tau+(/ to receive a larger impulse from a small force than from a lm -p shf8e6 r(eu;6(+kksag ng/m /et;sutpg,arge force? Explain.

A light object and a heavy object have the same kinetic energy. Which yz7w1nzog *qs9vb70de.lt62o )tqfu) p6h zy has the greater9 1 yvnoyh6z w) d70)qb tp.su7of qzgte2z*6l momentum? Explain.

Describe a collision in whi2b ,d:36 jrfuxnhf +yjch all kinetic energy is lost.

At a hydroelectric power plant, water1 qims31;ze bm :5vfhe is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to f1z:h3 imq1seeb5m;v a dead stop, or so that the water rebounds?

A squash ball hits a wyx-i;glrd xf:e ; m zx*4on,s2all at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped f 3mwv;/ir1 uvn 7e gsw8,h7oizrom a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and s u/ w7ivn iw sor;8h1g7mz,ve3ticks to the steel plate.

Why do you tend to ll zryxiib y.006f6)zxean backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is nothn-e9 nxit9 r) true for your arm xneht )9-nri9 or leg?

Show on a diagram how your CM shifts when yop6pkq*xbk 20z 0 g5xsou change from a lying position to a s206*zxp x50pgskq bok itting position.

If only an external force can change the momezp*zj9-(mwghiq s;h- ntum of the center of mass of an object, ho;- g*m-ipj(hz szqw9hw can the internal force of an engine accelerate a car?

A rocket following aznn z* )guks.c5 9vd m0h4gvb0 parabolic path through the air suddenly explodes into many pieces. What can you say about the motionv*zgg5nz hkc u4nm.)v9b0s d0 of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flva muema)a.fasv5je.l03 h10ying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction forcwodf3 l4qw uk,:7f/ dce of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in velocitdf7l/d3ocf u: q4,w wky?    m/s

  A 0.145-kg baseball pi+a: *dqdgyyb 6tched at 39 m/s is hit on a horizontal line drive straight back toward *aqddy6 +:ybgthe pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat thro)qah 2(j (yg hjx1p.nows a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat.p2oy xqah )n1 (h(gjj is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force yb :t tm1*-tfiexerted on a rocket, given that the propelling gases are expelled1im:*fby- ttt at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movingnq)*+*l6mgv2c 6lknwncm b3io ao9so *+e s7n at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on a*pvz uj:.l5 kzlevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be j pkz: luz*.v5the car’s new speed?    m/s

  A 9300-kg boxcar traveling i6la,,ky6hvpi- nn.y at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h If the casczm.hi8n,w2w 4o( air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the s.2c a(mw w i,no4zhc8force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s o5:z5 0sa 3a c. sxj97 /leeiaot/loqlun a level track. Snow begins to fall vertically and fills the car at a uaexol59/ stoe/5.7lz ij0: aqs3alcrate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha0-8 l vqbcsl9k1q jsip n:o*0j particle in the direction of its velocity, and the remaining nucleus sloqnv:jl8-o0kqcpilb sj1 * 09 sws to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg u31r) obio0 q*lr ees3block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, hrqs)o eubie331*l 0ro ow fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage roc ( 6in7zh95s bxwxfw0rket is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total masoefe9 f9f8r8 ns 3180 kg is traveling in outer space with a velocity of 115m/s To altn8 f 8r9oeff9eer its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is:;ppijon4 y8 vq f/ 0d0do/z k.m:xyzl hit off the tee at a speed of 45m/s The golf club was in contact with the ba8kd qy vjz4l0n xd0 :/f;/zpyop.iom:ll for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at amr 5gja90 qz stx7,;jm velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the imp5xg s0qjz;mr9ta 7m ,julse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0wq,p1;oextf) .06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new s0hvhkyy/ uwd qks0 )q217u8 z(zs1ixautomobile models. Cars are tested by smhqvuys1 yz1/ kq(0siz)u2w 8sd70 xhkashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the 6i,j0 wk p;lmx.a5ylleast and is stopped in 0.75 s by a head-on tackle by a tackler running due wew ;.y,0m5j6p lia llxkst. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mas2;z6fsx9c :u lal3t3q h ck2mys 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–qya2ll:k;96fcm3z2 t3c xuhs 33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lower*v a:jbes0cw9;aq9ho leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the stand0a *o:99qasw;cevhj bing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of 94-dc x1ls etfcollides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Lsfdlc 19-et4x et A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a a+ncs( km6syc9c ci+g /o3xb-i l7 8rpspeed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after t r 3/sok msg cl( c8-+a9xni6iy7cb+cphe collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfxg 14esc-c1c zo8zzfups04 *qectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the48oz40*uczccfsx- eg q1 z1sp positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving wit3 y jdlar,k6i-1 k ldcqth(4s*h a speed of 2.5m/s collides head-on with a 0.3* 1yak,di ksqr(jcd4l lh-6t090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is mop-ocnsv9 79d wving with a speed of 8.5m/s collides head-on and elastcn7p9d-vs o9wically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastic(*x/th 7 cjd sy5efax2ally as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and cd*yx sxf j/5cet7 (ha2ar B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second b7jag gwl/ *adz/ bz.x/ql/l5 6z/cv3woyq;yiall initi7/o3bcizlg/ywad;q *6q5lw z/va/y/j glz. xally at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionle lb - i-n) s)vlq(q-2azbgc5zmss incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does eacqa lb il2 -)nbzz5-m v(sq)g-ch cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objectl 4,lrjg+9dj n of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum h /t.yjavaw ed4kq ea;ca-6,7zeight h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum tay -6e dvaeataw;,j/kz4c.7 qo swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a hlw/4t1 hvc7 i3.6-kg pendulum hanging on a 2.8-m-long string, tvh 4c7wl1i/ hwhich makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lc+z 3(pjwa;ybost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at ref9tfdn7/ b0 .3ux 4vjspkh(d pst, into two pieces, one of which has 1.5 timevn u.f4j7(k/ 9dspbxd0 tf3hps the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at a vni :3 y6 oxwc0klm0z.red light. The bumpers lock, the brakes are locked, and the two cars skid forwar6i.0oyxzm3kwv0 lc:nd 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a he r::)09 hb gu1fivlewbight of 1.20 m. Approximi91 :rb0e gw:vhbu)lfately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objus)5 70dolyhg ects is the coefficient of restitution, 5s)7dlh 0gyou e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cutb.w.neh- ouoso75,g1 6ehb tg into two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and o,g.5-6 .1nh7sgewb ehoobu tthe fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x t9aq:ea.m tb7direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of aa9tbm.e : t7qeach mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest d+y4 ts --hudzvecays into a second nucleus, an electron, and a neutrino. The electron and neutrino are vs -+ dzyu4th-emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mas0.c* fneuga0 bs $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic cozxumnm )bd + lr1 27ojvzg937ollision between two objects of equal mass, each having initial speed the two bx+v9 3 z)jg z2d1r lm7mno7uomove off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rigsi*9:qpzb h ry1l m;5sht angles and meet at the origin of an xy coordinate system. Ball A is9h y b*15;l:zisspq mr moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) x5 nlk1qxkht:i4a(5.gw+zb:2 xtla emakes a perfectly elastic collision with another atom at rest. After the impact, the neon atom n zt(q1 txkl:5eax.54hkwigx2b:+altravels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastjjf a: dutn /21htwa0.ic collision with another atom at rest. After tj .dj1at2u t/wnfa0h: he impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-m28wyx+ ukm)q ymlebk6f1 oqy +0h- wn;ass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mah+8qm 10 w;yebfk y- 2ny +6qlmowu)xkss.    m

  The distance between a 3nbt4:ae1l(25.i6bk hdtxhfw auo ) rcarbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2. nd5-1lqyq/vin sp6y)50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seatq v-5nq)ilyns6/ 1d py 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raf 3 b1uvbowtjm)7 o88sdt, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy itvb7 1ob8mtjw 3)us od8s NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides:de0)k*s3 xjs zh35qoccs l p( $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato p;9duj z9 askw2aste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up thek s9dj ;wza92u load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut i e+wa7t gi0n,out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. W wt+i,07iang ehat is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those 1:r hu:/yo rfr3 geav.in Table 7–1, and calculate the mass of one of yurg/::h .y roa1ve3fr our legs.    kg

  Determine the CM of an outstretched arm using Table 7–xglbbe i s8)w r;gg7651.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bentbwv 5ng..uf5b at a right angle.g 55.ubwbn f.v Assume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positio(somvl++ em 5on such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be oummsvle+(oo + 5tside the body? Use Table 7–1.

The masses of the Earth and Moon aremh6wpot8bx n83om.06q 5cz 0.w tmjdz $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 6:ovf(*,yxz n nawss4m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg an7;rmd6 f nlw/sd a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectorfwm s l6dn7;/ry?    cm

  A mallet consists of afgnw3 -eq-2 2inm uo;s uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical ha- -ug oq;2n2sewn 3fimndle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Exampwip7vbv:r10j/t b cedu8u *3a le 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are5buum*,axey r6e -/ oq in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured w q*m -a 5xee/yob6,ruuith respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strizqznac 5to tqhll3 k;dy6*hq(-6(l7mkes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the avera(zol t 3m6q5 k7yzt-l( d6aqlnh hq;c*ge force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speedbdy;w hhll gw-r8n0-- $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced ), +lf3uy y6k-ibdks swith the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should k)ky,i6l-s+ yfsbd3uthe player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including spac) rp6i9 ;thvqee suit) acquires a speed of 2.5m/s by pushing off with his legs from an 180etq hir6v ;)p90-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at k(r/.w bg5 fmvrest in outer space. They then pm k5.vw/ rgf(bush each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a secjitv b81v(mq 6ond ball (at rest) and rebounds in the opposite directi mbi86vtj (v1qon with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involvi+f1 * eajwhhmx u56m1z m4ja+ong an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collis6j4*mzf1 5e+1x mwoj ahmh+uaion, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete y. 0+gkcht m :(7 bo5xqpin4pisteps of total vertical height 4.00 m. Tqoi(n y b+p :i 50mghk7c.pt4xhe ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired verticallb*q n 7+g r/hpnqyy8*uy into a 1.40-kg block of wood at rest directly above it. If the bulley/ np* 7qb*nrhugy+q 8t has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a rcdijp+rn8rj *. 96or1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle sp rjc+9rr8 j.6 dp*orineed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowbo2hc rn9p mmaf v,1*az6at of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction wi 6m2czpv9 fn1 ram,*ahll the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wasey 3wmgre0bbz 7bpc1 w+3 )0el about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken ap3xbkxd:(w3u 8wfzh 2i art into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the rx33kfzbu(2w8xd i w:hatio of their masses?   

  The force on a bullet is given by the fo wv3jtsfv+rkev 88s e3cr*8bvx 07l0/bj4n q trmula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses*e+enon d lsn*d-. s1c $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest des3((jf;hvi cge o-s a2w) pg2kcays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the )3wggkv-;(o(cj e 22h ifs sapalpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angr 2ysooe. afv(yi a):/p 2w9xile of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slide-6w + ck/hg(t )gucbuds down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is thogc1 +)z7 abby z(9ztae upper limit on mass m if it is to rebound from M, slide up the iny(a zztob9g1a 7 b)c+zcline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect.vnw:3 (jk8-f(mbpno y/j mtn3 Figure 7–47 shows the planet Saturn moving in the negative x direction at itsf8mnnv3 /o(:(ynm3 jwb- p jkt orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s